# The ALℓ0CORE Tensor Decomposition for Sparse Count Data

arXiv: https://arxiv.org/abs/2403.06153 · HTML: https://mlsanity.com/paper/2403.06153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 56 references that are in the map.
- First posted on arXiv 10 Mar 2024.

## Builds on (most cited first, 8 of 8)

- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relations](https://mlsanity.com/paper/1606.01855/) (2016)
- [Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Counts](https://mlsanity.com/paper/1506.03493/) (2015)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [A tensor factorization model of multilayer network interdependence](https://mlsanity.com/paper/2206.01804/) (2022)
- [Bayesian factorizations of big sparse tensors](https://mlsanity.com/paper/1306.1598/) (2013)
- [Equivariant and scale-free Tucker decomposition models](https://mlsanity.com/paper/1312.6397/) (2013)
- [The Ordered Matrix Dirichlet for State-Space Models](https://mlsanity.com/paper/2212.04130/) (2022)

## Abstract (arXiv)

This paper introduces ALℓ0CORE, a new form of probabilistic non-negative tensor decomposition. ALℓ0CORE is a Tucker decomposition where the number of non-zero elements (i.e., the ℓ0-norm) of the core tensor is constrained to a preset value Q much smaller than the size of the core. While the user dictates the total budget Q, the locations and values of the non-zero elements are latent variables and allocated across the core tensor during inference. ALℓ0CORE -- i.e., allocated ℓ0-constrained core-- thus enjoys both the computational tractability of CP decomposition and the qualitatively appealing latent structure of Tucker. In a suite of real-data experiments, we demonstrate that ALℓ0CORE typically requires only tiny fractions (e.g.,~1%) of the full core to achieve the same results as full Tucker decomposition at only a correspondingly tiny fraction of the cost.